The concentration equilibrium of polymer molecules with a porous medium was studied using a Jamin interferometer and digital image analysis. A porous silica bead was immersed into a solution of the polymer in a solvent isorefractive with silica. The concentration of the polymer in the porous medium was measured as the concentration in the exterior solution was changed in a wide range from dilute to semidilute. For all the chain dimensions studied, the partition coefficient increased to a value close to unity, as the exterior solution became semidilute, a result in agreement with theoretical predictions of the weak-to-strong penetration transition. The transition was, however, found to be more diffuse than predicted. The difference can be partly ascribed to a distribution in the effective pore diameter of the network-structured porous medium.